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%I #47 Apr 07 2020 23:33:32
%S 0,0,0,1,0,1,3,4,4,3,6,16,25,16,6,10,41,94,94,41,10,15,85,266,386,266,
%T 85,15,21,155,632,1247,1247,632,155,21,28,259,1332,3423,4657,3423,
%U 1332,259,28,36,406,2570,8342,14795,14795,8342,2570,406,36,45,606,4631,18546,41586,54219,41586,18546,4631,606,45
%N Array read by antidiagonals: T(m,n) = number of m X n matrices M with entries {0,1,2} that have M_{1,1}=0, M_{m,n}=2, are such that the rows and columns are monotonic without jumps of 2, and satisfy M_{(i+1),(j+1)} = M_{i,j} + (0 or 1).
%C The monotonicity condition requires that M_{(i+1),j} = M_{i,j} + (0 or 1); M_{i,(j+1)} = M_{i,j} + (0 or 1).
%C These matrices can be cut into three connected pieces, containing the 0's, 1's, and 2's; there are two vertex-disjoint paths from the north-and-east edges of the matrix to the south-and-west edges.
%C Row (or column) n >= 1 has a linear recurrence (with constant coefficients) of order 2n+1. - _Alois P. Heinz_, Feb 07 2019
%D D. E. Knuth, Email to N. J. A. Sloane, Feb 05 2019.
%H Alois P. Heinz, <a href="/A323846/b323846.txt">Antidiagonals n = 1..80, flattened</a>
%e Array begins:
%e 0 0 1 3 6 10 ...
%e 0 0 4 16 41 85 ...
%e 1 4 25 94 266 632 ...
%e 3 16 94 386 1247 3423 ...
%e 6 41 266 1247 4657 14795 ...
%e 10 85 632 3427 14795 54219 ...
%e ...
%e The 4 examples when m=2 and n=3 are
%e 011 011 012 012
%e 012 112 012 112
%Y Rows 1-10 give: A000217(n-2), A323847, A323967, A323968, A323969, A323970, A323971, A323972, A323973, A323974.
%Y Main diagonal gives A306322.
%Y Cf. A132823, A252876, A229428.
%K nonn,tabl
%O 1,7
%A _N. J. A. Sloane_, Feb 06 2019
%E More terms from _Alois P. Heinz_, Feb 07 2019
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